But even if Britain decided to leave the 28-nation bloc after
voting in the referendum on June 23, Simon Wells and his team at
HSBC warned that the UK is still likely to pay the EU for the
right to limit the movement of people coming across the border —
by being financially punished (emphasis ours):

According to opinion polls, the most widely cited reasons
for UK voters wanting to leave the EU are to stop the
UK's net contribution to the EU budget and to restrict EU
immigration.

This suggests that if the UK leaves the EU it would want
a divorce deal that allowed restrictions on labour
movement.

But the EU would be unlikely to offer the UK migration
restrictions without some quid pro quo.

Most likely it would seek to limit the freedom of
movement of capital and services, since these are areas where it
potentially would have most to gain and the UK a lot to
lose.

Various polls over the last year or so have shown how the Freedom
of Movement Act, which allows all EU citizens to easily migrate
to any other member state, as well as immigration in general, is
one of the factors that pushes UK voters to pip for exiting the
EU.

After all, government data shows that net migration into Britain
from the EU was 180,000 in the year to June 2015 — a new all-time
high.

However, of the 3.2 million non-UK nationals working in Britain
in the third quarter last year — just under 2 million were EU
nationals.

So if Britain was to curb migration and leave the EU, it would
hurt EU citizens the most. This is why Wells and his team at HSBC
believe that it's likely the EU would want something in return
for Britain restricting migration (emphasis ours):

Controls on the movement of capital and services would
cut both ways. Given its tight trade and geographic
links with the UK, Ireland's services exports to the UK are
around 3% of GDP, so it potentially would stand to lose out.

Otherwise, the big exporters of services to the UK (as a
proportion of the exporting countries' GDP) are EU economies with
either significant financial or tourism links to the UK (or in
the case of Cyprus and Malta possibly both).

HSBC

The EU is reliant on the UK for both the financial services it
produces, and its holidaymakers.

In 2014, the UK had a GBP17.1bn services trade surplus with the
rest of the EU. Within this, a GBP10.3bn deficit in travel
services is offset by a GBP10.8bn surplus in other, non-financial
services.

The UK's surplus in financial services trade (GBP16.6bn)
is roughly equal to the entire services surplus.

In the event of a UK vote to leave, the UK would be unlikely to
place restrictions on tourists, and countries in the EU that
benefit from UK tourists would be unlikely to impose significant
barriers. Therefore, it is financial services trade that would be
likely to be the focus in any post-Brexit negotiations.